[MT] REGRESSION ANALYSIS

A statistical technique that examines relationship between dependent (y) and one or more independent (x) variable

Regression Analysis

In a Regression Analysis, The relationship between x and y is described by ____________of the curve which best fits the data

means of an equation

A statistical technique that examines relationship between dependent (y) and one or more independent (x) variable

Regression Analysis

In a Regression Analysis, The relationship between x and y is described by ____________of the curve which best fits the data

means of an equation

Using the regression equation, values of independent variables (x) can be _____ in order to predict the values of dependent variable (y)

substituted

in regression analysis, The effect of each independent variable (x) on dependent variable (y) is measured by ______ and sign of the _____.

magnitude

regression coefficient

types of regression analysis

simple

multiple

linear

logistic

to determine and quantify the extent at which 1 quantitative variable (X) varies with another variable (Y), WITHOUT ASSUMING THAT Y IS DEPENDENT ON X (there is no dependent or indepent)

correlation

examines relationship between dependent (y) and one or more independent (x) variable (in regression, one variable is assumed dependent to the other variable)

regression

Relationship between X and Y is described by a single number, correlation coefficient

correlation

Relationship between X and Y is described by means of equation of the curve (to predict the value of Y based on a value of X)

regression

Effect of X to Y is measured by regression coefficient (magnitude and sign)

regression

Looks at linear relationship between 1 quantitative dependent variable (y) and one independent variable (x).

simple linear regression analysis

what symbol is the predicted value of dependent variable

y

what symbol is the the intercept, value of Y when X=0

a

what symbol is the slope of the line, measures the change in value of Y for every unit change in X

b

what symbol is the given value of IV

x

To determine how “good” the regression equation in predicting the values of Y based on X what are the 2 ways?

coefficient of determination

hypothesis testing

Measures the proportion of the total variability in the dependent variable (Y), that can be explained by, or attributed to the independent variable (X)

Coefficient of Determination (R2)

Measures the extent on how good it is to use the independent variable (X) to predict values of dependent variable (Y)

Coefficient of Determination (R²)

computed by getting the square of correlation coefficient,r.

Coefficient of Determination (R²)

𝜌

parameter of correlation coefficient

r

statistic of correlation coefficient

β

parameter of regression coefficient

b

statistic of regression coefficient

Correlation analysis is used to measure the ______ and ____ of the relationship between 2 quantitative variable, x and y

direction

strength

Regression analysis examines __________ relationship between dependent (y) and one or more independent (x) variable

cause and effect

_________ provides quantitative value to the strength and direction of the relationship between x and y

Correlation Coefficient (r)

Correlation analysis determined the direction depending on the ___ of r (positive or negative) and the strength of relationship based on the magnitude/value (0 to ±1.0)

sign

In___________, relationship between x and y is described by means of an equation of the curve which best fits the data: Y = a+bX

regression analysis

b = regression coefficent/slope, measures the change in value of _______ for every unit change in _____

YX variable

XY variable

Using the _________, values of independent variables can be substituted in order to predict the values of dependent variable

regression equation

The effect of IV to DV depends on the ___ and ________ of b.

sign and magnitude

_____________can be computed by getting the square of correlation coefficient, r

Coefficient of Determination (R2)

R2 measures the proportion of the ________ in the dependent variable (y), that can be explained by, or attributed to the independent variable (X)

total variability